The present book is devoted to a study of relative Prüfer rings and Manis valuations, with an eye to application in real and p-adic geometry. If one wants to expand on the usual algebraic geometry over a non-algebraically closed base field, e.g. a real closed field or p-adically closed field, one typically meets lots of valuation domains. Usually they are not discrete and hence not noetherian. Thus, for a further develomemt of real algebraic and real analytic geometry in particular, and certainly also rigid analytic and p-adic geometry, new chapters of commutative algebra are needed, often of a non-noetherian nature. The present volume presents one such chapter.
Lecture Notes in Mathematics Editors: J.–M. Morel, Cachan F. Takens, Groningen B. Teissier, Paris
1791
3 Berlin Heidelberg New York Barcelona Hong Kong London Milan Paris Tokyo
Manfred Knebusch Digen Zhang
Manis Valuations and Pru¨ fer Extensions I A New Chapter in Commutative Algebra
13
Authors Manfred Knebusch Digen ZHANG Department of Mathematics University of Regensburg Universit¨atstr. 31 93040 Regensburg Germany e-mail:
[email protected] [email protected]
Cover: "A good mathematician needs no counting rod", Lao Tse in Dao De Jing, chapter 27
Cataloging-in-Publication Data applied for. Die Deutsche Bibliothek - CIP-Einheitsaufnahme Knebusch, Manfred: Manis valuations and Prüfer extensions / Manfred Knebusch ; Digen Zhang. Berlin ; Heidelberg ; New York ; Barcelona ; Hong Kong ; Londo